CN107931743B - A kind of method of accurate control planar double enveloping worm transverse tooth thickness - Google Patents
A kind of method of accurate control planar double enveloping worm transverse tooth thickness Download PDFInfo
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- CN107931743B CN107931743B CN201711190980.6A CN201711190980A CN107931743B CN 107931743 B CN107931743 B CN 107931743B CN 201711190980 A CN201711190980 A CN 201711190980A CN 107931743 B CN107931743 B CN 107931743B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F19/00—Finishing gear teeth by other tools than those used for manufacturing gear teeth
- B23F19/002—Modifying the theoretical tooth flank form, e.g. crowning
Abstract
The present invention relates to a kind of control methods of transverse tooth thickness in planar double enveloping worm process, include: by worm screw clamping on grinding machine spindle, first using being ground planar double enveloping worm first lateral tooth flank by the way of worm axis rotary feed, first lateral tooth flank records main shaft angle after being ground out；Then by female flat inversed 180 degree, second lateral tooth flank is equally ground by the way of rotary feed, when main shaft goes to record angle in second lateral tooth flank grinding process, when two sides mother plane included angle is exactly setting value ε, the processing to the entire flank of tooth is completed, transverse tooth thickness has obtained accurate control.The present invention also just controls the sideshake of worm gear to effectively control worm screw transverse tooth thickness in process by solving and controlling the positional relationship of two sides mother's plane.This patent combines the theory of engagement and specific processing technology, and the control for worm gear sideshake is furthermore achieved in the accurate control by control realization of process parameters to transverse tooth thickness.
Description
[technical field]
The present invention relates to a kind of control methods of transverse tooth thickness in planar double enveloping worm process, specific to be exactly in fact
By solving and controlling the positional relationship of two sides mother's plane to make transverse tooth thickness meet design requirement.
[background technique]
The design of planar double enveloping worm transverse tooth thickness is the transverse tooth thickness design with reference to hindley worm, their indexing
Circular thickness s1=0.45pt, ptFor reference circle of wormwheel tooth pitch.The plane for crossing worm axis is referred to as axial plane of worm, for straight
Wide enveloping worm, the axial tooth profile that axial plane of worm intersects with the flank of tooth are straight line.Graduated arc and reality in axial plane of worm
Body two sides axial tooth profile intersects at two o'clock, as central angle γ=0.45 τ of this two o'clock and main basic circle circle center line connecting composition, indexing
Circular thickness is s1, wherein τ is angular pitch.Female plane needs to tilt centainly in the process of planar double enveloping worm
Angle, it is to become transverse tooth thickness, Changeable Lead, and throat's transverse tooth thickness is maximum that this, which results in the worm screw processed,.For planar double enveloping
The intersection of worm screw, axial plane of worm and female plane is straight line, and the axial tooth profile intersected with the flank of tooth is curve.Axial plane of worm
Interior worm indexing circular arc and entity two sides mother's plane intersect at two o'clock, the center of circle constituted in the presence of two intersection points and main basic circle circle center line connecting
When angle is γ=0.45 τ, the maximum tooth of the intersection point composition of two lateral tooth flank of entity obtained after worm indexing circular arc and actual processing
Thickness is less than s1.The manufacturing process of planar double enveloping worm is ground another again at present for 180 ° of bistrique overturning after one lateral tooth flank of grinding
Side, and the transverse tooth thickness of peri-laryngeal is measured, and as maximum tooth thickness, processing is terminated when measuring transverse tooth thickness and meeting design requirement,
The actual positional relationship of two sides mother plane is not considered.And with the continuous propulsion of feeding, maximum tooth thickness is in worm screw circumference side
Upward position constantly changes, and causes to look for inaccurate there are maximum tooth thickness position in measurement process, measures the problem of transverse tooth thickness inaccuracy.
For Double enveloping hourglass worm gearing, the sideshake of worm gear is also by control worm screw relative to hobboing cutter
Reducing thickness is come what is realized, and when worm screw transverse tooth thickness cannot be controlled accurately, the sideshake of worm gear is also difficult to control.
[summary of the invention]
In view of the above technical problems, a kind of method of accurate control planar double enveloping worm transverse tooth thickness is provided.
To achieve the above object, a kind of method of accurate control planar double enveloping worm transverse tooth thickness is designed, which is characterized in that
The theory of engagement and specific processing technology are combined, by solving and controlling the positional relationship of two sides mother's plane, realized to transverse tooth thickness
Accurate control, further realize the control for worm gear sideshake；
Its method and step includes: by worm screw clamping on grinding machine spindle, first using along the side of worm axis rotary feed
Formula is ground planar double enveloping worm first lateral tooth flank, and first lateral tooth flank records main shaft angle after being ground out；It then will be female flat inversed
180 degree is equally ground second lateral tooth flank by the way of rotary feed, when main shaft goes to record angle in second lateral tooth flank grinding process
When, when two sides mother plane included angle is exactly setting value ε, the processing to the entire flank of tooth is completed, transverse tooth thickness has obtained accurate control.
The calculation method of the mother plane included angle setting value ε are as follows:
Step 1: the two sides mother plane included angle α of initial value ε=2+162/Z in setting axial plane of worm2, wherein α is reference circle
Pressure angle, Z2For the worm gear number of teeth；
Step 2: being established initial according to two sides mother plane included angle according to Principles of Gear Connection and homogeneous coordinate transformation matrix
First, the second two sides tooth surface equation obtained after value processing；
Step 3: solving two lateral tooth flank of entity and graduated arc intersection point in axial plane of worm, and calculate the arc of point-to-point transmission
Long s；
Step 4: from the inlet to the outlet along worm screw circumferencial direction, arc is found in arc length when from worm screw difference angular position
Long maximum value is denoted as maxs, then reduction in tooth thickness Δ s1=s1- maxs, s1For graduated arc transverse tooth thickness design value；
Step 5: if Δ s1Less than setting value δ, then calculating is terminated, δ is tooth thickness error iteration ends differentiation amount；Otherwise ε is enabled
=ε+Δ s1/r2, r2For worm indexing arc radius, turn the first step, substitutes into equation and solve Δ s again1, item is set until meeting
Until part.
Remember that u, v are female plane parameter,WithRespectively female plane and worm screw rotational angle, β are female planar inclination, rbFor
Main base radius, a1Center when for machining worm is away from, i01Transmission ratio when for machining worm, (x0,y0,z0) it is in female plane
The coordinate of point, (x1,y1,z1) it is the coordinate put on the planar double enveloping worm flank of tooth.
The then equation of first lateral tooth flank are as follows:
The equation of second lateral tooth flank are as follows:
A kind of method of accurate control planar double enveloping worm transverse tooth thickness as claimed in claim 2, which is characterized in that snail
Point in bar axial plane on graduated arc should meet equation:
θ corresponds to the different angular positions of worm screw, and the friendship of available graduated arc Yu the first flank of tooth is even stood in equation (3) and (1)
Point (x11,y11,z11)；The intersection point of equation (3) and (2) Lian Li, available graduated arc and the second flank of tooth is denoted as (x12,y12,z12),
The arc length of point-to-point transmission:
The present invention is by solving and controlling the positional relationship of two sides mother's plane, to effectively control snail in process
Bar transverse tooth thickness also just controls the sideshake of worm gear.This patent combines the theory of engagement and specific processing technology, by controlling work
Skill parameter realizes the accurate control to transverse tooth thickness, and the control of the sideshake for worm gear is furthermore achieved.
[Detailed description of the invention]
Fig. 1 is two sides mother plane relation schematic diagram
Fig. 2 is maximum tooth thickness schematic diagram
Fig. 3 is transverse tooth thickness change curve schematic diagram
Fig. 4 is that female plane included angle setting value solves flow chart
[specific embodiment]
Technical solution of the present invention is further elaborated now in conjunction with accompanying drawings and embodiments, it is believed that those skilled in the art
For be clear.
By worm screw clamping on grinding machine spindle, first using being ground planar envelope ring by the way of worm axis rotary feed
Surface-worm first lateral tooth flank, first lateral tooth flank record main shaft angle after being ground out；Then same using circle by female flat inversed 180 degree
The mode that week feeds is ground second lateral tooth flank, when main shaft goes to record angle in second lateral tooth flank grinding process, two sides mother's plane holder
When angle is exactly setting value ε, the processing to the entire flank of tooth is completed, transverse tooth thickness has obtained accurate control.
The calculation method of angle setting value ε are as follows:
Step 1: the entity two sides mother plane included angle α of initial value ε=2+162/Z in setting axial plane of worm2.Wherein α is point
Spend circle pressure angle, Z2For the worm gear number of teeth；
Step 2: being established initial according to two sides mother plane included angle according to Principles of Gear Connection and homogeneous coordinate transformation matrix
First, the second two sides tooth surface equation obtained after value processing；
Step 3: solving two lateral tooth flank of entity and graduated arc intersection point in axial plane of worm, and calculate the arc of point-to-point transmission
Long s；
Step 4: from the inlet to the outlet along worm screw circumferencial direction, arc length is found most in arc length when from different angular positions
Big value is denoted as maxs.Then reduction in tooth thickness Δ s1=s1- maxs, s1For graduated arc transverse tooth thickness design value；
Step 5: if Δ s1Less than setting value δ, then calculating is terminated, δ is tooth thickness error iteration ends differentiation amount；Otherwise ε is enabled
=ε+Δ s1/r2, r2For worm indexing arc radius, turn the first step, substitutes into equation and solve Δ s again1, item is set until meeting
Until part.
When processing two lateral tooth flanks, mother plane included angle is ε, transverse tooth thickness has obtained accurate control.
Embodiment
For center away from a1=125, transmission ratio i01=40, female planar inclination β=10 °, reference diameter d1=50, main base
Radius of circle rb=40, worm gear tooth number Z2=40, enveloping teeth zk=4, worm indexing circular thickness s1=7.069, pressure angle α=
The planar double enveloping worm of 23.578 ° of angular pitch τ=9 °, taking and terminating differentiation amount δ is 0.005.According to Principles of Gear Connection and
Homogeneous coordinate transformation matrix, the equation of the first flank of tooth are as follows:
The equation of the second flank of tooth are as follows:
The α of initial value ε=2+162/Z2=51.2060, the female flat relation of plane in two sides is as shown in Figure 1.Divide in axial plane of worm
Point on degree circular arc should meet equation:
θ corresponds to the different angular positions of worm screw.Equation 3 and 1 even founds the intersection point of available graduated arc Yu the first flank of tooth
(x11,y11,z11)；Equation 3 and 2 is even vertical, and the intersection point of available graduated arc and the second flank of tooth is denoted as (x12,y12,z12).Point-to-point transmission
Arc length:
When φ value is (- zk/2, zk/2), θ=- i10(α+(φ+0.225) τ), available a series of s.Wherein
Maximum value maxs=6.625.As shown in Fig. 2, heavy line is the intersection of axial plane of worm and female plane, it is straight line.Fine line is
The intersection of two sides tooth form after axial plane of worm and actual processing is curve.Δ s can be obtained by further calculating1=0.444,
Δs1> δ, therefore enable ε=51.461 °, brings into again and executes operation and obtain Δ s1=-0.002, meets design requirement.
Assuming that main shaft angle is 0 degree when the grinding of first lateral tooth flank finishes.Bistrique is ground second lateral tooth flank after overturning 180 degree.When into
When main shaft angle is 0 degree after giving, two sides mother plane included angle ε=51.461 °.Then worm screw transverse tooth thickness change curve after molding is such as
Shown in Fig. 3, maximum tooth thickness 7.069.
Claims (4)
1. a kind of method of accurate control planar double enveloping worm transverse tooth thickness, which is characterized in that by the theory of engagement and specific processing
Technique combines, and by solving and controlling the positional relationship of two sides mother's plane, realizes the accurate control to transverse tooth thickness, further realizes
Control for worm gear sideshake；
Its method and step includes: to grind first using by the way of worm axis rotary feed by worm screw clamping on grinding machine spindle
The face of scabbling double enveloping worm first lateral tooth flank, first lateral tooth flank record main shaft angle after being ground out；Then by mother flat inversed 180
Degree, is equally ground second lateral tooth flank by the way of rotary feed, when main shaft goes to record angle in second lateral tooth flank grinding process,
When two sides mother plane included angle is exactly setting value ε, completion has obtained accurate control to the processing transverse tooth thickness of the entire flank of tooth.
2. a kind of method of accurate control planar double enveloping worm transverse tooth thickness as described in claim 1, which is characterized in that described
The calculation method of female plane included angle setting value ε are as follows:
Step 1: the entity two sides mother plane included angle α of initial value ε=2+162/Z in setting axial plane of worm2, wherein α is reference circle
Pressure angle, Z2For the worm gear number of teeth；
Step 2: foundation adds according to two sides mother plane included angle initial value according to Principles of Gear Connection and homogeneous coordinate transformation matrix
First, the second two sides tooth surface equation obtained after work；
Step 3: solving two lateral tooth flank of entity and graduated arc intersection point in axial plane of worm, and calculate the arc length s of point-to-point transmission；
Step 4: from the inlet to the outlet along worm screw circumferencial direction, arc length is found most in arc length when from worm screw difference angular position
Big value is denoted as maxs, then reduction in tooth thickness Δ s1=s1- maxs, s1For graduated arc transverse tooth thickness design value；
Step 5: if Δ s1Less than setting value δ, then calculating is terminated, δ is tooth thickness error iteration ends differentiation amount；Otherwise enable ε=ε+
Δs1/r2, r2For worm indexing arc radius, turn the first step, substitutes into equation and solve Δ s again1, it is until meeting to impose a condition
Only.
3. a kind of method of accurate control planar double enveloping worm transverse tooth thickness as claimed in claim 2, which is characterized in that note u,
V is female plane parameter,WithRespectively female plane and worm screw rotational angle, β are female planar inclination, rbFor main base radius, a1
Center when for machining worm is away from, i01Transmission ratio when for machining worm, (x0,y0,z0) be female Plane-point coordinate, (x1,
y1,z1) it is the coordinate put on worm tooth-surface, the equation of first lateral tooth flank are as follows:
The equation of second lateral tooth flank are as follows:
4. a kind of method of accurate control planar double enveloping worm transverse tooth thickness as claimed in claim 3, which is characterized in that worm screw
Point in axial plane on graduated arc should meet equation:
θ corresponds to the different angular positions of worm screw, and the intersection point of available graduated arc Yu the first flank of tooth is even found in equation (3) and (1)
(x11,y11,z11)；The intersection point of equation (3) and (2) Lian Li, available graduated arc and the second flank of tooth is denoted as (x12,y12,z12), two
Arc length between point:
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| CN111536218B (en) * | 2020-05-15 | 2023-03-24 | 重庆大学 | Point-line evolvable enveloping worm transmission pair and working mode thereof |
| CN112525040B (en) * | 2020-11-26 | 2022-07-05 | 上海合纵重工机械有限公司 | Tooth thickness gauge for plane enveloping ring surface worm and manufacturing method and using method thereof |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CA654610A (en) * | 1962-12-25 | E. Birtch Fred | Method and apparatus for grinding double-enveloping worm elements | |
| CN86107189A (en) * | 1986-10-13 | 1987-05-20 | 冶金部西安冶金机械厂 | The processing method of ring surface-worm with envelop curved face |
| CN103752954A (en) * | 2013-12-31 | 2014-04-30 | 重庆机床(集团)有限责任公司 | Machining method of worm gear with straight profile helical surface |
| CN104148745A (en) * | 2014-08-12 | 2014-11-19 | 西华大学 | Online detection and correction machining method for enveloping worm tooth surface |
| CN106064255A (en) * | 2016-07-26 | 2016-11-02 | 上海合纵重工机械有限公司 | A kind of method being homogenized planar double enveloping worm flank of tooth grinding allowance |
| CN106909729A (en) * | 2017-02-21 | 2017-06-30 | 河北涞博传动机械制造有限公司 | The method of adjustment of Double-conical-surface double enveloping worm emery wheel |
-
2017
- 2017-11-24 CN CN201711190980.6A patent/CN107931743B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CA654610A (en) * | 1962-12-25 | E. Birtch Fred | Method and apparatus for grinding double-enveloping worm elements | |
| CN86107189A (en) * | 1986-10-13 | 1987-05-20 | 冶金部西安冶金机械厂 | The processing method of ring surface-worm with envelop curved face |
| CN103752954A (en) * | 2013-12-31 | 2014-04-30 | 重庆机床(集团)有限责任公司 | Machining method of worm gear with straight profile helical surface |
| CN104148745A (en) * | 2014-08-12 | 2014-11-19 | 西华大学 | Online detection and correction machining method for enveloping worm tooth surface |
| CN106064255A (en) * | 2016-07-26 | 2016-11-02 | 上海合纵重工机械有限公司 | A kind of method being homogenized planar double enveloping worm flank of tooth grinding allowance |
| CN106909729A (en) * | 2017-02-21 | 2017-06-30 | 河北涞博传动机械制造有限公司 | The method of adjustment of Double-conical-surface double enveloping worm emery wheel |
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